The procedure for MaxUp is taken from [1]}: For each data point \(x_i\)  in the original training set \(\mathcal {D} = \lbrace (x_i, y_i)\rbrace _{i=1}^n\) , a set \(\lbrace \tilde{x}_{i,j}\rbrace _{j=1}^{m}\)  of augmented data points are produced. Learning is defined according to a modified ERM,
\(\min _{\theta }\mathbb {E}_{x \sim \mathcal {D}}[\max _{j}\mathcal {L}(\tilde{x}_{i,j}, \theta )].\) 
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